If $y(x)=\cot^{-1}\!\left(\dfrac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right),\; x\in\left(\tfrac{\pi}{2},\pi\right)$, then $\dfrac{dy}{dx}$ at $x=\tfrac{5\pi}{6}$ is: